Model Results
June 24, 2019
I. Summary statistics and trace plots
##
## Iterations = 105010:120000
## Thinning interval = 10
## Number of chains = 3
## Sample size per chain = 1500
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## alpha.p[1] 2.91715 0.15168 0.002261 0.002261
## alpha.p[2] 3.00976 0.17129 0.002553 0.003065
## alpha.p[3] 1.82537 0.09324 0.001390 0.001390
## beta.repro.gamma[1] 1.24844 0.37153 0.005538 0.009039
## beta.repro.gamma[2] 2.09554 0.41723 0.006220 0.012672
## beta.repro.gamma[3] 0.78915 0.43977 0.006556 0.007498
## beta.repro.gamma[4] 0.39880 0.38402 0.005725 0.007707
## beta.repro.phi[1] 1.67960 0.40987 0.006110 0.010687
## beta.repro.phi[2] 0.94146 0.32070 0.004781 0.006889
## beta.repro.phi[3] 0.03826 0.49545 0.007386 0.009994
## beta.repro.phi[4] 0.55898 0.30671 0.004572 0.005487
## beta.rgr.gamma[1] -0.21580 0.12976 0.001934 0.002281
## beta.rgr.gamma[2] 0.09966 0.12385 0.001846 0.002984
## beta.rgr.phi[1] 0.02314 0.17124 0.002553 0.003702
## beta.rgr.phi[2] -0.12046 0.10787 0.001608 0.001638
## beta.d.gamma[1] 0.60192 0.15362 0.002290 0.002440
## beta.d.gamma[2] 5.48693 1.03769 0.015469 0.101622
## beta.d.p[1] 0.89585 0.24346 0.003629 0.003658
## beta.d.p[2] 0.96074 0.30539 0.004552 0.005481
## beta.d.p[3] 0.44147 0.09487 0.001414 0.001465
## beta.d.phi[1] 0.23406 0.11098 0.001654 0.001687
## beta.d.phi[2] 0.75160 0.29840 0.004448 0.005120
## beta.d.psi[1] 1.34199 0.18900 0.002817 0.003320
## beta.d.psi[2] 1.75418 0.20977 0.003127 0.004558
## mu.gamma[1] -2.32775 0.34190 0.005097 0.009462
## mu.gamma[2] -3.02206 0.41084 0.006125 0.013849
## mu.gamma[3] 3.61873 0.77205 0.011509 0.066458
## mu.gamma[4] 3.59564 0.72827 0.010856 0.065766
## mu.phi[1] -0.35789 0.38012 0.005666 0.011868
## mu.phi[2] 0.22133 0.30210 0.004504 0.008098
## mu.phi[3] 1.95298 0.41526 0.006190 0.011071
## mu.phi[4] 1.57203 0.23931 0.003567 0.005524
## mu.psi[1] -0.16899 0.20725 0.003089 0.003349
## mu.psi[2] 0.25089 0.19389 0.002890 0.003123
## mu.psi[3] 1.50218 0.23363 0.003483 0.005159
## mu.psi[4] 1.40405 0.16919 0.002522 0.004386
## sigma.gamma 0.98639 0.15687 0.002338 0.005689
## sigma.phi 0.92391 0.17669 0.002634 0.007452
## sigma.psi[1] 1.08785 0.20299 0.003026 0.005519
## sigma.psi[2] 0.73828 0.19920 0.002969 0.008740
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## alpha.p[1] 2.62667 2.80881 2.91650 3.01852 3.22703
## alpha.p[2] 2.69529 2.88956 3.00617 3.12138 3.35906
## alpha.p[3] 1.64449 1.76263 1.82513 1.88840 2.00587
## beta.repro.gamma[1] 0.53413 0.99615 1.24145 1.49872 1.98888
## beta.repro.gamma[2] 1.32163 1.80119 2.08052 2.37140 2.95731
## beta.repro.gamma[3] -0.03415 0.48717 0.77958 1.07635 1.69064
## beta.repro.gamma[4] -0.33965 0.13761 0.39778 0.66228 1.14629
## beta.repro.phi[1] 0.90613 1.40448 1.67091 1.95607 2.49460
## beta.repro.phi[2] 0.32602 0.73147 0.93723 1.14811 1.59328
## beta.repro.phi[3] -0.92263 -0.29393 0.04660 0.37585 1.01055
## beta.repro.phi[4] -0.03689 0.35073 0.55900 0.76851 1.16716
## beta.rgr.gamma[1] -0.47650 -0.30324 -0.21335 -0.12870 0.03164
## beta.rgr.gamma[2] -0.13348 0.01657 0.09727 0.18092 0.35344
## beta.rgr.phi[1] -0.30804 -0.08904 0.01992 0.13765 0.35840
## beta.rgr.phi[2] -0.32802 -0.19452 -0.12223 -0.05096 0.10276
## beta.d.gamma[1] 0.31172 0.49882 0.60135 0.70205 0.90360
## beta.d.gamma[2] 3.74607 4.70500 5.39357 6.16768 7.70185
## beta.d.p[1] 0.44064 0.72333 0.89198 1.06000 1.38579
## beta.d.p[2] 0.39707 0.74820 0.95167 1.16226 1.59031
## beta.d.p[3] 0.26286 0.37655 0.44060 0.50261 0.63314
## beta.d.phi[1] 0.02384 0.15764 0.23425 0.30700 0.45566
## beta.d.phi[2] 0.19752 0.54665 0.74107 0.94446 1.36071
## beta.d.psi[1] 0.98811 1.21055 1.33494 1.46481 1.73056
## beta.d.psi[2] 1.36394 1.60671 1.75231 1.89176 2.17581
## mu.gamma[1] -3.03859 -2.55048 -2.31626 -2.09438 -1.70433
## mu.gamma[2] -3.89526 -3.28014 -3.00122 -2.73481 -2.27199
## mu.gamma[3] 2.26178 3.04180 3.56447 4.13581 5.16608
## mu.gamma[4] 2.36735 3.04246 3.53996 4.07209 5.14876
## mu.phi[1] -1.11715 -0.60858 -0.35894 -0.10603 0.39451
## mu.phi[2] -0.37957 0.01675 0.22358 0.42387 0.81019
## mu.phi[3] 1.18547 1.66482 1.93290 2.20831 2.81974
## mu.phi[4] 1.12471 1.40592 1.56303 1.73149 2.05410
## mu.psi[1] -0.58748 -0.30446 -0.16883 -0.03087 0.23223
## mu.psi[2] -0.13088 0.12514 0.25010 0.37993 0.63287
## mu.psi[3] 1.07171 1.34170 1.49130 1.65350 1.99132
## mu.psi[4] 1.09034 1.29185 1.39575 1.51214 1.76066
## sigma.gamma 0.70094 0.87679 0.97697 1.08589 1.32029
## sigma.phi 0.58651 0.80190 0.91903 1.03918 1.28802
## sigma.psi[1] 0.70994 0.95087 1.08278 1.21974 1.51472
## sigma.psi[2] 0.37503 0.59868 0.73175 0.86904 1.14977II. Gelman-Rubin diagnostic
## Potential scale reduction factors:
##
## Point est. Upper C.I.
## alpha.p[1] 1.00 1.00
## alpha.p[2] 1.00 1.00
## alpha.p[3] 1.00 1.00
## beta.repro.gamma[1] 1.00 1.01
## beta.repro.gamma[2] 1.00 1.00
## beta.repro.gamma[3] 1.00 1.00
## beta.repro.gamma[4] 1.00 1.01
## beta.repro.phi[1] 1.00 1.00
## beta.repro.phi[2] 1.00 1.00
## beta.repro.phi[3] 1.00 1.00
## beta.repro.phi[4] 1.00 1.00
## beta.rgr.gamma[1] 1.00 1.00
## beta.rgr.gamma[2] 1.00 1.01
## beta.rgr.phi[1] 1.00 1.00
## beta.rgr.phi[2] 1.00 1.00
## beta.d.gamma[1] 1.00 1.00
## beta.d.gamma[2] 1.02 1.06
## beta.d.p[1] 1.00 1.00
## beta.d.p[2] 1.00 1.00
## beta.d.p[3] 1.00 1.00
## beta.d.phi[1] 1.00 1.00
## beta.d.phi[2] 1.00 1.00
## beta.d.psi[1] 1.00 1.00
## beta.d.psi[2] 1.00 1.01
## mu.gamma[1] 1.00 1.01
## mu.gamma[2] 1.00 1.00
## mu.gamma[3] 1.02 1.06
## mu.gamma[4] 1.02 1.07
## mu.phi[1] 1.00 1.00
## mu.phi[2] 1.00 1.00
## mu.phi[3] 1.00 1.00
## mu.phi[4] 1.00 1.01
## mu.psi[1] 1.00 1.00
## mu.psi[2] 1.00 1.01
## mu.psi[3] 1.00 1.00
## mu.psi[4] 1.00 1.01
## sigma.gamma 1.00 1.01
## sigma.phi 1.00 1.01
## sigma.psi[1] 1.00 1.01
## sigma.psi[2] 1.02 1.06
##
## Multivariate psrf
##
## 1.03III. Posterior predictive check
Scatterplot of summed squared residuals. The Bayesian posterior predictive check p-value was 0.37.